k-Ordered Hamilton cycles in digraphs

Authors:
Daniela Kühn;Deryk Osthus;Andrew Young
Affiliations:
School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK;School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK;School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
Venue:
Journal of Combinatorial Theory Series B
Year:
2008

Citing 5
Cited 1

k-linked and k-cyclic digraphs

Journal of Combinatorial Theory Series B
k-Ordered Hamiltonian graphs

Journal of Graph Theory
On Sufficient Degree Conditions for a Graph to be $k$-linked

Combinatorics, Probability and Computing
On k-ordered Hamiltonian graphs

Journal of Graph Theory
Degree conditions for k-ordered hamiltonian graphs

Journal of Graph Theory

A survey on Hamilton cycles in directed graphs

European Journal of Combinatorics

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Abstract

Given a digraph D, let @d^0(D):=min{@d^+(D),@d^-(D)} be the minimum semi-degree of D. D is k-ordered Hamiltonian if for every sequence s"1,...,s"k of distinct vertices of D there is a directed Hamilton cycle which encounters s"1,...,s"k in this order. Our main result is that every digraph D of sufficiently large order n with @d^0(D)=@?(n+k)/2@?-1 is k-ordered Hamiltonian. The bound on the minimum semi-degree is best possible. An undirected version of this result was proved earlier by Kierstead, Sarkozy and Selkow [H. Kierstead, G. Sarkozy, S. Selkow, On k-ordered Hamiltonian graphs, J. Graph Theory 32 (1999) 17-25].